What is the solution for f^'(x)= 1/(1+\frac{1){1+1/(1+x)}} ?

The solution for f^'(x)= 1/(1+\frac{1){1+1/(1+x)}} is f(x)= 1/2 x+3/4+1/4 ln(2x+3)+c_{1}

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f^'(x)= 1/(1+\frac{1){1+1/(1+x)}}

f^{^{'}} (x) = \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + x}}}

f (x) = \frac{1}{2} x + \frac{3}{4} + \frac{1}{4} ln (2 x + 3) + c_{1}

Solution steps

f^{'} (x) = \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + x}}}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + x}}} d x

\int \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + x}}} d x = \frac{1}{2} x + \frac{3}{4} + \frac{1}{4} ln (2 x + 3) + c_{1}

f (x) = \frac{1}{2} x + \frac{3}{4} + \frac{1}{4} ln (2 x + 3) + c_{1}

What is the solution for f^'(x)= 1/(1+\frac{1){1+1/(1+x)}} ?
The solution for f^'(x)= 1/(1+\frac{1){1+1/(1+x)}} is f(x)= 1/2 x+3/4+1/4 ln(2x+3)+c_{1}